Finite Group Databasebeta

← #28347073

Subgroups — #28347073

Order 13696.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293244C212yesmaximal, complemented
2#20293024C211yesmaximal, characteristic, complemented
3#20293010C211yesmaximal, characteristic, complemented
4#20292985C212yesmaximal, complemented
5#20292885C211yesmaximal, characteristic, complemented
6#20292854C212yesmaximal, complemented
7#20292739C211yesmaximal, characteristic, complemented
8#20292733C211yesmaximal, characteristic, complemented
9#20292718C212yesmaximal, complemented
10#20292585C211yesmaximal, characteristic, complemented
11#469×C107C211yesmaximal, characteristic
12C2×Dic428C2211yescharacteristic
13C2×#13133806C2212yes—
14C22×C107⋊C8C2211yescharacteristic
15#16812108C2212yes—
16#16812102—22no—
17#16812096—22no—
18#16812096C2212yes—
19#16812090—22no—
20#16812088C2212yes—
21#16812086—22no—
22#16812074C2212yes—
23D4×Dic107C2212yes—
24#16812068C2211yescharacteristic
25#16812041C2211yescharacteristic
26#16812040C2212yes—
27#16812034C2212yes—
28#16812032C2212yes—
29#16812030C2212yes—
30#16812019C2211yescharacteristic
31#16812019C2211yescharacteristic
32C8×Dic107C2211yescharacteristic
33C8×Dic107C2211yescharacteristic
34C2×D8×C107C2211yescharacteristic
35C2×M16×C107C2211yescharacteristic
36#121×C107C2212yes—
37#106×C107C2211yescharacteristic
38#102×C107C2212yes—
39C2×Dic214—22no—
40C2×Dic214C2312yes—
41C22×Dic107—22no—
42Dic428—22no—
43#13133806—24no—
44C2×C107⋊C8—22no—
45C2×C107⋊C8C2311yescharacteristic
46C2×C107⋊C8C2311yescharacteristic
47C4⋊Dic107D412yes—
48C4⋊Dic107C2312yes—
49Dic107⋊C4—22no—
50Dic107⋊C4—22no—
51Dic107⋊C4—22no—
52C22⋊Dic107—22no—
53C22⋊Dic107—22no—
54C22⋊Dic107—22no—
55C22⋊Dic107—22no—
56C22⋊Dic107D412yes—
57C4×Dic107—22no—
58C4×Dic107C2311yescharacteristic
59C4×Dic107C2311yescharacteristic
60C2×D4×C107—22no—
61C2×D4×C107C2312yes—
62C22×C4×C107C2311yescharacteristic
63D8×C107—22no—
64M16×C107—22no—
65C2×C8×C107C2311yescharacteristic
66C2×C8×C107C2311yescharacteristic
67C4⋊C4×C107C2312yes—
68C22⋊C4×C107—22no—
69C23×C107—22no—
70C23×C107C2×D411yescharacteristic
71D4×C107—22no—
72D4×C107—22no—
73D4×C107—82no—
74C2×C4×C107—21no—
75C2×C4×C107—21no—
76C2×C4×C107—22no—
77C2×C4×C107C2×D411yescharacteristic
78C2×C4×C107C2411yescharacteristic
79C2×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107—82no—
82C2×Dic107C2×D412yes—
83C2×Dic107C2×D412yes—
84Dic214—22no—
85Dic214—22no—
86Dic214—82no—
87C8×C107—21no—
88C8×C107#4112yes—
89C107⋊C8—21no—
90C107⋊C8#4112yes—
91C22×C107—21no—
92C22×C107—22no—
93C22×C107—42no—
94C22×C107—42no—
95C22×C107—42no—
96C22×C107C22×D411yescharacteristic
97C4×C107—21no—
98C4×C107—42no—
99C4×C107C2×#4111yescharacteristic
100C4×C107C2×#4111yescharacteristic
101Dic107—22no—
102Dic107—22no—
103Dic107—42no—
104Dic107—42no—
105C2×C107—41no—
106C2×C107—82no—
107C2×C107#53211yescharacteristic
108C2×C107#57712yes—
109#3173—1071nomaximal, Sylow
110C107#317311yescharacteristic, complemented, Sylow
111#542—1072no—
112#498—1071no—
113#495—1071no—
114#489—1072no—
115#470—1071no—
116#469D10711yescharacteristic
117#465—1072no—
118#442—1071no—
119#441—1071no—
120C4×SD16—1072no—
121#405—1071no—
122C2×Q16—1071no—
123C2×SD16—1072no—
124C2×D8C2×D10711yescharacteristic
125C2×M16C2×D10711yescharacteristic
126C22×C8—1071no—
127C4⋊Q8—1072no—
128#126—2142no—
129#124—1072no—
130#124—2142no—
131#123—2142no—
132C22⋊Q8—1072no—
133C22⋊Q8—2142no—
134#121C2×D10712yes—
135C4×Q8—1072no—
136C4×D4—1072no—
137#117—1071no—
138#106—1071no—
139#106—1072no—
140#106C2×D10711yescharacteristic
141#103—1072no—
142#103—1072no—
143#102—1072no—
144#102C2×D10712yes—
145#97—1071no—
146#97—1071no—
147C4×C8—1071no—
148C4×C8—1071no—
149C2×Q8—1072no—
150C2×Q8—2142no—
151C2×D4—22no—
152C2×D4C22×D10712yes—
153C22×C4—2142no—
154C22×C4C22×D10711yescharacteristic
155Q16—2142no—
156SD16—2144no—
157D8—22no—
158M16—22no—
159C2×C8—1071no—
160C2×C8—1071no—
161C2×C8—2142no—
162C2×C8C22×D10711yescharacteristic
163C2×C8C22×D10711yescharacteristic
164C4⋊C4—1072no—
165C4⋊C4—1072no—
166C4⋊C4—2142no—
167C4⋊C4—2142no—
168C4⋊C4—2142no—
169C4⋊C4C22×D10712yes—
170C22⋊C4—22no—
171C22⋊C4—1072no—
172C22⋊C4—2142no—
173C22⋊C4—2142no—
174C22⋊C4—2142no—
175C22⋊C4—2142no—
176C42—1071no—
177C42—1071no—
178C42—2142no—
179C23—22no—
180C23D4×D10711yescharacteristic
181Q8—8562no—
182Q8—2142no—
183Q8—2142no—
184D4—22no—
185D4—22no—
186D4—82no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—8562no—
191C2×C4—1072no—
192C2×C4—1072no—
193C2×C4—2142no—
194C2×C4—2142no—
195C2×C4D4×D10711yescharacteristic
196C2×C4C23×D10711yescharacteristic
197C8—21no—
198C8—1072no—
199C8—2141no—
200C8#1313381712yes—
201C22—21no—
202C22—22no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C2×D4×D10711yescharacteristic
207C4—21no—
208C4—42no—
209C4—4282no—
210C4—4282no—
211C4—2142no—
212C4—2142no—
213C4#41×D10711yescharacteristic
214C4C2×#1313381711yescharacteristic
215C2—41no—
216C2—82no—
217C2#2029317211yescharacteristic
218C2#2029343712yes—
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting, prime radical#469×C107C2
socleC22×C107C22×D4
hypercenter#469D107
hypocenterC107#3173
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20293244C2semidirect
2. #20293024C2semidirect
3. #20293010C2semidirect
4. #20292985C2semidirect
5. #20292885C2semidirect
6. #20292854C2semidirect
7. #20292739C2semidirect
8. #20292733C2semidirect
9. #20292718C2semidirect
10. #20292585C2semidirect
110. C107#3173semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202932442
#202930242
#202930102
#202929852
#202928852
#202928542
#202927392
#202927332
#202927182
#202925852
#469×C1072
#3173107